1. Field of the Invention
The present disclosure generally relates to an apparatus and method for estimating a Doppler shift for underwater communication and, more particularly, to an apparatus and method for estimating a Doppler shift for underwater communication, which may estimate a Doppler shift by computing correlations between output values of a matched filter and using a time gap between points at which the correlations have maximum values.
2. Description of the Related Art
In terrestrial and underwater radio communications, a Doppler shift occurs by relative movements of communication devices. The Doppler shift increases relative to an increase in approaching or receding speed of a relative distance between the transmitter and receiver according to the Doppler effect.
For example, a wavelength of light changes according to movement of an object, i.e., it becomes longer as the object moves farther away and becomes shorter as the object moves closer.
While a Doppler shift occurs, respective frequency components of a signal undergo different Doppler shifts and the length of the signal becomes long or short relative to an amount of the Doppler shift. To quantitatively represent the Doppler shift, a relative Doppler shift, Δ, is used, which may be expressed in the following equation 1:Δ=v/c  (1)
where, v is a relative difference in moving speed between the transmitter and the receiver, and c is the velocity of waves in the medium. Due to the Doppler shift, distortions may occur in the received signal on the time axis r(t) and the frequency axis fD, which may be expressed in the following equations 2 and 3, respectively:r(t)=s((1+Δ)t)  (2)fD=f(1+Δ)  (3)
where s(t) is a signal for transmission, r(t) is a Doppler-shifted received signal, f is one of frequency components of the signal for transmission of a bandwidth, and fD is a frequency component resulting from a Doppler shift of the frequency component f.
In terrestrial radio communications using radio waves, the speed of waves c is defined to be approximately 3×108 m/s, which is the same as the speed of light. Generally, in terrestrial radio communications, signals having a few kHz to tens of MHz of bandwidth are transmitted at a carrier frequency of hundreds of MHz to a few GHz. For example, in the case of Automatic Identification System (AIS) used in the safe operation of vessels, communication data is transmitted at a frequency around 160 MHz of carrier frequency on a channel having a bandwidth of 25 kHz. Furthermore, assuming that the relative moving speed between the transmitter and receiver is about 15 m/s (or 54 km/h), the relative Doppler shift Δ has a very small value. Since packet signals typically used in radio communications are about tens of ms long, an amount of increase or decrease in signal length resulting from the Doppler shift is very small in one packet length, and thus the distortions occurring on the time axis can often be ignored. However, the carrier frequency used for terrestrial communications is about within a few MHz to a few GHz, and the signal may be distorted due to distortions occurring on the frequency axis from the Doppler shift. A frequency band of signals used for terrestrial communications is a narrow band having a relatively small ratio of carrier frequency to bandwidth, which is often less than a few percentage of the carrier frequency. Accordingly, all frequency components in the signal band may be approximated to the carrier frequency to be subject to the same Doppler shift. In terrestrial narrow band communication, such a Doppler shift is approximately considered as a carrier frequency error, which is estimated and compensated using a frequency-shift synchronization method.
Since a velocity of waves in a medium that transmits information in underwater communication using sound waves is about 1500 m/s, and the velocity of waves in a medium in terrestrial communication is about 3×108 m/s, a Doppler shift in underwater communication using sound waves may appear to be 2×106 times greater than in terrestrial radio communication that uses radio waves at the same relative difference in moving speed between the transmitter and the receiver.
In underwater communication using sound waves, a carrier frequency is about from a few kHz to tens of kHz, and the usage bandwidth of the signal becomes up to tens of percentage of the carrier frequency, that is, the underwater communication signal is a wideband signal. In underwater communication, the wideband signal may lead to occurrence of different frequency shifts at the same Doppler shift for respective frequency components of the signal, and may thus be more appropriately approximated with a change in length of a received packet signal due to the Doppler shift in the time domain. The Doppler shifted received packet signal is expressed in the equation 2.
FIG. 1 shows a structure of a packet signal for underwater communication. Referring to FIG. 1, in conventional underwater communication using wideband signals, in order to estimate a Doppler shift, known signals 10 and 30 are transmitted by being placed at either ends of packet data 20 with a known length, and the receiver uses a method for estimating the Doppler shift based on a time gap TRX (between two signal points where peak values of outputs of matched filtering of the known signals from a matched filter appear, a time gap TTX between the two known signals, and a relationship with the Doppler shift, as expressed in equation 4.
Equation 4 is as follows:
                              Δ          ^                =                                            T              RX                        -                          T              TX                                            T            TX                                              (        4        )            
where, TTX is a gap between signals transmitted to estimate a Doppler shift, and TRX (is a time gap between two points that represent peak values of outputs of a matched filter in the receiver, which may be greater or smaller than TTX according to the Doppler shift.
In underwater communication using sound waves, as previously described, the known signals 10 and 30, known to be robust to Doppler shift, are placed at either ends of the packet data 20, or placed with a predetermined interval, and the receiver uses a method for estimating a Doppler shift by measuring a time gap between two peak values of outputs of a matched filter.
The method may be suitably used when there is an Additive White Gaussian Noise (AWGN) channel or when one path among multipaths has a much larger energy than others. However, underwater channel conditions are characterized in that there may be similar size multipath components, that the multipath components with a sparse distribution arrive at the receiver end, and that the multipath components are changed in size over time, that is, time-varying channel response. In the time-varying multipath underwater channel condition, if there are multipath components having similar magnitude, peak values of the outputs of the matched filter corresponding to the front and rear parts of the packet may be determined based on respective different paths due to the variation of the magnitude of the multipath components.
FIG. 2 shows an instance of occurrence of an error in estimation of a Doppler shift using conventional estimator when there are similar size multipaths. In the case that there are two multipaths with similar sizes in the reception of a signal having a structure of a packet signal 100 of FIG. 2, when a known signal 1 110 and a known signal 2 130 are received, the sizes of the respective multipaths and a difference in arrival time are represented in FIG. 2 by solid and dashed arrows for the two multipaths, respectively. As can be seen from FIG. 2, the path represented by the solid line has the largest size in receiving the known signal 1 110, and the path represented by the dashed line has the largest size in receiving the known signal 2 130. In this case, using the aforementioned method for estimating a Doppler shift commonly used in underwater communication causes an error in estimation of the Doppler shift. In other words, an error occurs in measurement of the time gap between the two peak values, leading to an error in estimation of the Doppler shift.